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Homework Help: An inequality, in need of help.

  1. Feb 6, 2006 #1

    MathematicalPhysicist

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    Gold Member

    i need to prove that if x>y>0 and n>1 n natural then:
    n(x-y)y^(n-1)<x^n-y^n<n(x-y)x^(n-1)

    i tried almost everything from n(x^n-y^n)/x-y>(x^n-y^n)/x-y>1

    but to get nothing, can someone help?
     
  2. jcsd
  3. Feb 6, 2006 #2

    HallsofIvy

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    You know, do you not, that xn- yn= (x- y)(xn-1+ xn-2y+ ...+ xyn-2+ yn-1)?
     
    Last edited by a moderator: Feb 6, 2006
  4. Feb 6, 2006 #3

    MathematicalPhysicist

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    Gold Member

    well thanks.
     
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